Limit classification of a real quadratic form of an ordinary second order self adjoint differential expression (Q1821245)

A classification of differential expressions \(Ly=-y(2)+qy\), depending on the number of square-integrable solutions of \(Ly=\lambda y\) for im \(\lambda\neq 0\), is well known. Similar classification of the differential expressions \(L^ 2y=L(Ly)\) can be obtained having the knowledge of the classification of L. Here the classification of \(aL^ 2+bL+c\), where a,b,c are real constants, is determined, the classification of L being known.